Problem: Solve for $x$ : $4x^2 + 40x + 36 = 0$
Answer: Dividing both sides by $4$ gives: $ x^2 + {10}x + {9} = 0 $ The coefficient on the $x$ term is $10$ and the constant term is $9$ , so we need to find two numbers that add up to $10$ and multiply to $9$ The two numbers $1$ and $9$ satisfy both conditions: $ {1} + {9} = {10} $ $ {1} \times {9} = {9} $ $(x + {1}) (x + {9}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 1) (x + 9) = 0$ $x + 1 = 0$ or $x + 9 = 0$ Thus, $x = -1$ and $x = -9$ are the solutions.